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In differential geometry, a Clifford module bundle, a bundle of Clifford modules or just Clifford module is a vector bundle whose fibers are Clifford modules, the representations of Clifford algebras. The canonical example is a spinor bundle.〔Berline et al (2004) pp.113-115〕〔Lawson & Michelsohn (1989) pp.96-97〕 In fact, on a Spin manifold, every Clifford module is obtained by twisting the spinor bundle. The notion "Clifford module bundle" should not be confused with a Clifford bundle, which is a bundle of Clifford algebras. ==Spinor bundles== (詳細はirreducible Clifford modules over ''Cℓ''(''T'' *''M''). In fact, such a bundle can be constructed if and only if ''M'' is a spin manifold. Let ''M'' be an ''n''-dimensional spin manifold with spin structure ''F''Spin(''M'') → ''F''SO(''M'') on ''M''. Given any ''Cℓ''''n''R-module ''V'' one can construct the associated spinor bundle : where σ : Spin(''n'') → GL(''V'') is the representation of Spin(''n'') given by left multiplication on ''S''. Such a spinor bundle is said to be ''real'', ''complex'', ''graded'' or ''ungraded'' according to whether on not ''V'' has the corresponding property. Sections of ''S''(''M'') are called spinors on ''M''. Given a spinor bundle ''S''(''M'') there is a natural bundle map : which is given by left multiplication on each fiber. The spinor bundle ''S''(''M'') is therefore a bundle of Clifford modules over ''Cℓ''(''T'' *''M''). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「clifford module bundle」の詳細全文を読む スポンサード リンク
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